207 
acceleration is given, and the other that it is exactly proportional 
to the acceleration when the mass is given. After assigning to the 
two factors appropriate units, their product constitutes the analy- 
tical symbol which is universally employed m calculations relating 
to the effects of moving force. The hypothesis of the exactness of 
the proportions suggested by the experiments is abundantly verified 
by comparisons of the calculated results with experimental facts 
It may! further, be remarked, as a corollary to this argument that 
it verifies two of the fundamental qualities of matter ; its mobility, 
by showing that it is capable of being moved by force, and its 
inertia by showing that it requires force to move it. 
26. Considering the special object of this essay as. expressed by 
its title and the usual character of the communications made to 
this Society, it would be altogether inappropriate to enter into 
details respecting the mathematical reasoning of which the adopted 
definitions of the atoms and the ether form the basis. Neither, as 
far as regards the exhibition of the general argument, is there any 
occasion' to do so ; but it will be necessary to state some of the 
principal results. Kespecting these it is important to make t ie 
preliminary remark, that as they are deduced from definitions that 
are intelligible from sensation and experience , they are theoreticat 
results in the strict sense of that term,— the sense it has by being 
derived from Qtwpui, viewing. By modern physicists ie wor 
Theory is used in various senses, as, especially, to denote the re- 
presentation by formulae, however obtained, of the experimental 
laws of physical phenomena ; but its proper scientific meaning, is 
that in which it is applicable, as just mentioned, in the Newtonian 
system of physical and metaphysical philosophy. Now since, as 1 
have already said, this philosophy has not been adopted, or carrie 
on, by any of my contemporaries, it follows that I am alone respon- 
sible for the deductions from it which I am about to state. 1 nese 
are results which have been obtained by mathematical reasoning 
from precisely defined premises ; and although, as must be ad- 
mitted, the application of the mathematics is attended with 
difficulties, and the reasoning is for the most part of . a nove 
and high order, the results may, I think, lay claim to consideration 
on the ground of being the fruits of labours devoted to the solu- 
tion of hydrodynamical problems through a long course ot yeais. 
At all events, I hope by means of the subjoined, statements, 
whether or not they be assented to, to indicate what is the actua 
position of physical science, and to remove some prevailing misap- 
prehensions as to its character and objects. . 
27. The following inferences, deduced mathematically from t e 
adopted definitions of the atoms and the ffither, are stated heie as 
being of chief importance relative to the conclusions that will su 
